Raffael Stenzel abstract


Title: Complete Bousfield-Segal spaces as a model of Homotopy Type Theory


Abstract: Complete Segal spaces were introduced by Charles Rezk to formalize a notion of infinity-categories. Indeed, as shown by Joyal and Tierney, the homotopy theory of complete Segal spaces is equivalent to the homotopy theory of quasi-categories. Complete Bousfield-Segal spaces, introduced under that name by Julia Bergner, are the groupoidal version of complete Segal spaces, in the same way as Kan complexes are the groupoidal version of quasi-categories. Complete Bousfield-Segal spaces have been studied by several authors such as Dugger and Cisinski from different viewpoints under different names. The aim of the talk is to give an introduction to complete Bousfield-Segal spaces as the fibrant objects in a model structure that is right proper and validates the univalence axiom, and that is equivalent to the model structure for Kan complexes. We will also discuss the connection between Rezk’s notion of completeness and the type theoretical notion of univalence, and, if time allows, consider connections to further references and applications.


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